名校
解题方法
1 . 抛物线
与直线
相交于
两个不同的点.
(1)当
时,求线段
的长;
(2)若
,求直线
的斜率
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd55f837e9c4e6bba1163ef13edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02f266bd253738e315e84231235f0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2 . 如图,过抛物线
的焦点F的直线交抛物线于点A,B,交其准线l于点C,若F是
的中点,且
,则线段
的长为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/bcb36f9d-2b0b-4b5a-a864-3ee36b4e8fe7.png?resizew=156)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6d8eaacc2d999b37209feba103f9ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb5437739f67f04669e00f6cc09e7a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/24/bcb36f9d-2b0b-4b5a-a864-3ee36b4e8fe7.png?resizew=156)
A.5 | B.6 | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
3 . 已知动圆
过定点
,且与直线
相切,圆心
的轨迹为
.
(1)求动点C的轨迹方程;
(2)已知直线
交轨迹E于两点P,Q,且
中点的纵坐标为2,则
的最大值为多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5421a28dc3675ae20190d6090793246e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bacd1449fbdfec7ee01526d7b6233e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求动点C的轨迹方程;
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
2023-05-31更新
|
185次组卷
|
2卷引用:第二章圆锥曲线 单元测试题-2021-2022学年高二上学期数学北师大版(2019)选择性必修第一册
解题方法
4 . 已知抛物线关于
轴对称,它的顶点在坐标原点,并且经过点
.
(1)求抛物线的标准方程;
(2)若斜率为
的直线
经过抛物线的焦点
,且与抛物线相交于
,
两点,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73eeee75206e9fa425330f40d94e6f7.png)
(1)求抛物线的标准方程;
(2)若斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
您最近一年使用:0次
解题方法
5 . 如图,设抛物线
的焦点为
,准线为
,过点
的直线交抛物线
于
两点,交
于点
,且
是
的中点,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a900c464141ed36bbe1908e2a54b528.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098658ddd8826dc6637297e1e6c7acdc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/13/c9f0da2b-b256-4158-aaf6-d1b1d359146a.png?resizew=198)
A.2 | B.![]() | C.5 | D.![]() |
您最近一年使用:0次
2023-08-12更新
|
423次组卷
|
3卷引用:云南省绥江县第一中学2020-2021学年高二下学期期中考试数学(文)试题
6 . 如图所示,抛物线
,AB为过焦点F的弦,过A,B分别作抛物线的切线,两切线交于点M,设
,
,
,则下列结论正确的有( )
![](https://img.xkw.com/dksih/QBM/2023/4/16/3217763738501120/3250132541628416/STEM/d0d824ad8c5d44d0a5eaf75aa78a91bf.png?resizew=120)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4564dc28307341aea4003be38c19dfdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfc04d299bab9f4acc3a856854ceb77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bc97d4acc37ccb7480571754737cbc.png)
![](https://img.xkw.com/dksih/QBM/2023/4/16/3217763738501120/3250132541628416/STEM/d0d824ad8c5d44d0a5eaf75aa78a91bf.png?resizew=120)
A.若AB的斜率为1,则![]() |
B.![]() |
C.![]() |
D.若AB的斜率为1,则![]() |
您最近一年使用:0次
解题方法
7 . 如图所示,某桥是抛物线形拱桥,当水面在
时,拱顶离水面
,水面宽
.水位下降
后,水面宽为_____ 米;已知经过上述抛物线焦点且斜率为2的直线交抛物线于A,B两点,则A,B两点间的距离|AB|=_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f71a41641aa0d0e45a3c03d3d2c1196b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7854968bbf6576a1fd9926ee0d4d63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f328ba89c0a92a4447788b65571f7aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/3/376fca14-f5ea-462c-b6cd-3c21057ad958.png?resizew=144)
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8 . 过抛物线y2=2px(p>0)的焦点F作弦AB,其所在直线的倾斜角为
,则|AB|等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3427311203b1958b9ff89084c66a09a.png)
A.![]() | B.4p | C.6p | D.8p |
您最近一年使用:0次
解题方法
9 . 过点
作斜率为2的直线
,交抛物线
于
两点,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a29ba49963134a7232fa8574105fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88bee8e70f1fab639be1636c7bce0477.png)
A.4 | B.5 | C.6 | D.7 |
您最近一年使用:0次
2023-04-05更新
|
407次组卷
|
2卷引用:广西横州市横州中学2020-2021学年高二下学期4月段考数学试题
10 . 已知抛物线
的焦点为
,过点
且斜率为
的直线
与抛物线
交于A(点A在第二象限),
两点,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ed2bede8fe8ec670cac3a085b80cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16961fbed865cc8408bea83a9bee35ed.png)
A.![]() | B.![]() | C.4 | D.5 |
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